1

Steel Bridge Connection Design

Karl H. Frank

Hirschfeld Industries

Outline

• Connection Limit States Shear Connections• Connection Limit States-Shear Connections

• Connection Design Forces-Composite Girders

• Design Example

2

Limit States- Shear Connections• Bolt Strength

– Shear• Threads Out of the Shear Plane

• Threads in the Shear Plane

– Slip• Bolt Tension

• Slip Coefficient

• Connected Material– Bolt Bearing

– Net and Gross Section

– Block Shear

Bolt Shear StrengthuF x 0.60Material ofStrength Shear

Threads Not

Excluded from Shear

Plane

Threads Excluded

from Shear Plane

bolt

bolt

A 0.8ExcludedNot Threads

AExlcuded Threads

:AreaShear

Lengthin inches 50 to UpJointsfor Factor Reduction Connection - 0.80

StrengthShear x AreaShear x 0.8StrengthShear Bolt

3

Unequal Bolt Shear In Long Joints

Bolt ShShear

Joint Length Shear Strength Reductions

Design Strength/ Single Bolt Capacity

0.80

0.80x0.80=0.64

1

Design Spec.

Connection Length50 in.

4

Bolt Shear Strength

Threads Threads

Excludede dsNot

Excluded from Shear

Plane

Excluded from Shear

Plane

boltu

boltu

A x F 0.38

A x 0.8 x F x .600 x 0.8

:StrengthShear

boltu

boltu

A x F 0.48

A x F x .600 x 0.8

:StrengthShear

s=0.80

ts shn PN K KRCapacity Slip

Kh= Hole Factor= 1 (normal size holes)

s=1.0(Art.6.13.2.2)

Tension InstalledBolt

Pt

Ks= Surface Condition Slip Coefficient=0.5(blasted or Zinc Rich)

Ns=Number of Slip Planes per Bolt

utensile

t

F x A x 0.70

StrengthTensile x 0.70P

5

Post Slip Examination of Zinc Rich Paint Specimen

6

Diameter (in.)

0.625 0.75 0.875 1 1.125 1.25 1.375

Ab (in2) 0.307 0.442 0.601 0.785 0.994 1.227 1.485

A325 Bolt

Fub (ksi) 120 120 120 120 105 105 105

Fub Ab (kip) 36.8 53.0 72.2 94.2 104.4 128.9 155.9

Pt (kip) 19 28 39 51 56 71 85

Type sRn (kip)

A325F 9.5 14.0 19.5 25.5 28.0 35.5 42.5

A325N 11.2 16.1 21.9 28.7 31.7 39.2 47.4

A325X 14.1 20.4 27.7 36.2 40.1 49.5 59.9

7

Diameter (in.)

0.625 0.75 0.875 1 1.125 1.25 1.375

Ab (in2) 0.307 0.442 0.601 0.785 0.994 1.227 1.485

A490 Bolt

Fub (ksi) 150 150 150 150 150 150 150

Fub Ab (kip) 46.0 66.3 90.2 117.8 149.1 184.1 222.7

Pt (kip) 24 35 49 64 80 102 121

Type sRn (kip)

A490F 12.0 17.5 24.5 32.0 40.0 51.0 60.5

A490N 14.0 20.1 27.4 35.8 45.3 56.0 67.7

A490X 17.7 25.4 34.6 45.2 57.3 70.7 85.5

Undeveloped Filler

Bending of Bolts Reduces Shear Strength

8

Filler at Flange Thickness Transitiontf

γ1

0.25in. tif

:FillertodueReduction Strength Shear

f

Af= Sum of the Area of the Filler Plates

tp

p

f

t

t

normally A

A γ

2γ1

γ1R

p

f

Ap= Smaller of Connected Plate Area or Sum of Splice Plate Area

Bearing Strength of Connected Material Standard Holes

ucn

un

c

F t L 1.2R

d 2Lfor

F t d 2.4R

d 2L if

d

Lc x 0.6Fu

LcLc

bb=0.80

9

AASHTO Bearing Strength 

Fu= 65ksi Hole Size=Dia.+0.0625

Diameter (in.) 0.625 0.75 0.875 1 1.125 1.25 1.375

Min. Spacing (in.) 1.875 2.25 2.625 3 3.375 3.75 4.125

Clear Distance (in.) 1.188 1.438 1.688 1.938 2.188 2.438 2.688

bbRn (kip/in. of thickness) 74.1 89.7 105.3 120.9 136.5 152.1 167.7

Typical Spacing (in.) 2 2.5 3 3 3.5 3.75 4.25

Clear Distance (in.) 1.313 1.688 2.063 1.938 2.313 2.438 2.813

bbRn (kip/in. of thickness) 81.9 105.3 128.7 124.8 144.3 156 175.5

A325X/Bearing 0 17 0 19 0 22 0 29 0 28 0 32 0 34A325X/Bearing 0.17 0.19 0.22 0.29 0.28 0.32 0.34

A490X/Bearing 0.22 0.24 0.27 0.36 0.40 0.45 0.49

Min. End Distance (in.) 0.875 1 1.125 1.25 1.5 1.625 1.75

Clear Distance (in.) 0.53 0.59 0.66 0.72 0.91 0.97 1.03

bbRn (kip/in. of thickness) 33.15 37.05 40.95 44.85 56.55 60.45 64.35

bb=0.80

Design Conditions

• Dead Load and Service Load II Design• Dead Load and Service Load II- Design Against Slip

• Strength I- Design for Shear, Bearing, Block Shear, and Net Section

• Minimum Connection- Controls for many C C yfield Splices

10

Minimum Connection- Web ShearArticle 6.13.6.1.4b

• If Vu< 0.5 v Vn (Shear at Strength I less ½ shear capacity)

– Vuw= 1.5 x Vu

Oth i• Otherwise:

2

V φVV nvu

uw

Minimum Flange Force Controlling Flange (largest stress)

Ax FForceFlangeMinimum ecf

flangen compressioAA

F φ α 0.752

F φ αRf

F

g

ge

yff

yffh

cf

cf

ecf

flangetension AAFφ

F φgnet

yty

uu

11

Controlling Flange RequirementsRh =1

fli50G dAA1 09

flangen compressioAA

F 0.752

F fF

Ax FForceFlange Minimum

ge

yfyfcf

cf

ecf

flangen 50W tensio Grade AA 1.18

flangetension 50GradeAA 1.09

gnet

gnet

Non Controlling Flange

A x FForce Flange Minimum enf

flangencompressioAA

flange gcontrollinfor stressdesign in increase f

FR

F φ α 0.75R

fRF

cf

cfcf

yffh

nfcfnf

flangetension AAFφ

F φ

flangen compressioAA

gnetyty

uu

ge

12

Design Forces Web SpliceMoment in Web

RcffncfNon Controlling

Flangeg

R F

= +

RhFcfControlling Flange

Connection Design Stress in Web

(RhFcf +Rcffncf)/2 (RhFcf -Rcffncf)/2

Axial Force Moment

Web Connection Design Forces

Vuwuw

Huw= [(RhFcf +Rcffncf)/2]x tw D

Muw=[(RhFcf -Rcffncf)/2]x tw D2/6

Two Rows Minimum

e=eccentricity of Vuw

13

Web Connection Design Force

Moment:

M V + MM= Vuwx e + Muw

Vertical Force:

V=Vuw

Horizontal Force:

H= Huw

• Calculate Force on Corner Fastener Using Rigid Body Equations Assuming Rotation About Centroid of Bolt Group

Web Corner Bolt Shear

mn 1mg1ns12

mn I 2222

p

n= number of bolts in one vertical rowm= number of vertical rows

uwuwuw 1mMVeVFV ti lV

s

g

22

p

uwuwuw

p

uwuwuw

HVShearBolt Maximum

s2

1n

I

MV e

nm

HForce HorizontalH

g2Inm

ForceVerticalV

H

V

14

NHI Girder Splice Example

Nominal Forces

ForceService

IIStrength

IA grossII I gross

Web Shear Force-198.53

kip262.2 kip

Stress Top Flange Mid Thickness

-0.73 ksi -1.32 ksi14x3/4=

10.50

Stress Bottom Flange Mid Thickness

15.1 ksi 20.69 ksi14x7/8=

12.25Controls

15

Controlling Flange RequirementsTension Flange, Rh =1

5020 69Ff ff

in8.977

x15

x412.25A

holes. standard web,of sideeach bolts in.8

7of Rows Two

ksi 37.5F 0.7535.32

5020.69

2

F fF

2t

yfyfcf

cf

kip 366.69.77 x 37.5ForceDesign Splice

in 12.25A9.771.09x8.75A 1.09A

in8.978

x16

x 412.25A

2gnete

net

Non Controlling Compression Flange

Flange gControllin Increase of Ratio 1.81 20 69

37.5

f

FR cf

cf

ksi37 550x1x1x0 75

F φ α 0.752.181

1.32 1.81

R

fRF

A x FForce Flange Minimum

20.69f

yffh

nfcfnf

enf

cfcf

kip 394.810.5 x 37.5ForceDesign Splice

flangen compressio in 10.5AA

ksi37.550x 1x 1x 0.752

ge

16

Bottom Flange Bolt Strength½ in.

7/8 in.

5701γ1

57.0875.0

5.0 γ

in 2

1

8

7

8

31in t

8

7t

:0.25in. tsinceFiller todueReduction Strength Shear

sf

f

kip 20.227.7 x 0.73StrengthShear Bolt

Excluded ThreadsBolt with A325in 8

7

73.00.57 x 21

57.01

2γ1

γ1R

Top Flange Bolt Strength½ in.

¾ in.

6701γ1

67.075.0

5.0 γ

in 2

1

4

3

4

11in t

4

3t

:0.25in. tsinceFiller todueReduction Strength Shear

sf

f

kip .89127.7 x 0.71StrengthShear Bolt

Excluded ThreadsBolt with A325in 8

7

71.00.67 x 21

67.01

2γ1

γ1R

17

Bolt Requirements

Splice Bolt Bearing Bearing

Bearing Based on 1.5 in. End Distance

ConnectionDesign Force

kip

Shear Capacity

kip

Number of Bolts Required

Number Provided

BearingForce/Bolt

kip

BearingEnd Bolt

Flange kip

Top Flange 394.8 19.8394.8/(2x19.8)=

9.9612

394.8/12=32.9

64.35x ¾= 48.3 OK

Bottom Flange

357.8 20.2366.6/(2x20.2)=

9.0712

366.6/12=30.5

64.35x 7/8= 56.3 OK

tsplice= should be greater than half the smaller flange thicknessTop Flange tsplice>= 0.5x3/4 use 7/16 in.

Bottom Flange tsplice>= 0.5x7/8 use 7/16 in.

Web Connection Shear • Unstiffened Web-k=5, D=54,tw=0.5, D/tw =108

– Vn= C Vp , Vp= 0.58x50x54x0.5=783 kip

0.39

50

29,000x5

0.554

1.57

F

Ek

tD

1.57C 2

yw2

w

kips 283.8

2

305.4262.2

2

VφVV

kip 152.7Vφ 0.5262.2V

kip305.4783 x 0.39V

nvuuw

nvu

n

18

Web Connection Moment:

Muw=[(RhFcf -Rcffncf)/2]x tw D2/6

=[1x37.5-1.81x-1.32]x 0.5 x 542/12

= 4,847 k-in

Vuwx e = 283.8 x 3.25= 922.4 k-ine=1.5 in. hole edge distance in web+ half the 1/2 in. space between

webs(1/4 in.) + half the 3 in. row spacing in connection (1.5 in.) =3.25

Total Moment=4,847+922.4=5,769 k-in

Web Connection Horizontal Force:

Huw= [(RhFcf +Rcffncf)/2]x tw D= [(1x37.5+1.81x-1.32)/2]x0.5x54=474.0 kip

Web Corner Bolt Shear

2222

2222p

123113312

2 x 15

1mg1ns12

mn I

Try:n= number of bolts in one vertical row=15m= number of vertical rows=2

Connection H i h 14 3 42 i 2in 5,108

1nMVeHH

kip 11.232

12

5,108

4,847283.8 x 3.25

30

283.8

g2

1m

I

MV e

nm

VV

uwuwuw

p

uwuwuw

Height=14x3=42 in.

3 in.

3in

(A325N) kip 43.8 2x21.9 kip 41.1

5.9311.2HVShearBolt Maximum

kip 5.9332

115

5,882

4,847922

30

474

s2Inm

H

2222

p

uwuwuw

19

Contributions of Various Forces Upon Web Bolt Force

Force V kip H kipVuw 9.46 0

e x Vuw 0.27 3.8Muw 1.4 19.9Huw 0 15.8

Total 11.13 39.5Total 11.13 39.5

Additional Checks

• Bearing on Web Connection• Bearing on Web Connection

• Block Shear

• Net Section

• Slip During Construction and Fatigue LoadingLoading

20

g1

Block Shear Modes

L

g1

g1

L

holes drilled 1R

AFU 0.58Rφ

AFUAF 0.58RφR

p

tnubspbs

tnubsvnupbsr

vgy AF

bs=0.80Avn

Atn

L

g1

sL

g2

bending 0.5

force axial 1U

frames) (cross

holes punched 0.9

bs

p

Good and Bad

1.Too Many Web Bolts ~72 boltsBolts 72 bolts

2. End Distance on Flange Splice Plate?

21

Good and Bad

Two Rows in Web,

Higher Shear in Outer Girder

(Curved Bridge)

Questions?